A rational number is any number that can be expressed as the quotient a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number.

OR

can be defined by (a,b) ~ (c,d) if, and only if, a*d - b*c = 0

("~" is the equivalence relation)

that is to say, a/b = c/d <=> a*d - b*c = 0

Can you show that every positive rational number can be written as a quotient of products of factorials of (not necessarily distinct) prime numbers?

For example, 10/9 = (2!*5!) / (3!*3!*3!)

How would you write 5/7 ?

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